2-4 Standard Valence-Bond Theory for N2O and F2O2
21
any bond that arises from electron sharing by two atoms. The concept of an energy
stabilization through resonance between two or more Lewis structures was
developed by Pauling and Slater in the early 1930s. For references to this period,
the reader is referred to Ref. (1b), p.184.
Lewis also suggested that when carbon, nitrogen, oxygen and fluorine atoms
are bonded to other atoms in a molecule, they tend to acquire the electron configuration of the inert gas neon. With a
2
2
6
1s 2s 2p ground-state configuration, the
neon atom has eight electrons in its valence shell. When they form covalent bonds,
atoms of the other elements above acquire this neon configuraton, by sharing their
unpaired electrons with the unpaired electrons of other atoms. According to
Lewis, stable (or low energy) valence-bond structures have eight valence-shell
electrons disposed around the atomic kernels (atomic nuclei + inner-shell electrons) for any of these first-row elements. Lewis and Langmuir respectively gave
the names of “rule of eight” and “octet rule” to this requirement. One quantum
mechanical justification for this rule is provided by the existence of four n = 2 atomic orbitals (namely 2s,
x
2p , y
2p , and z
2p ), and a maximum occupancy of two
electrons per orbital is permitted by the Pauli exclusion principle.
2-4(b) Standard Valence-Bond Theory and N 2 O
We shall now use the covalent molecule N 2 O to consider how the octet rule is
usually applied. For this molecule, there are nine Lewis structures (namely structures (1)-(9) of Figure 2-9) that have different π-electron distributions, and which
satisfy the octet rule. Each of these structures will contribute to the ground state
resonance description of the electronic structure
ii
. To provide a simple qualitative
discussion of the bonding, it is usual to select those valence-bond structures that
are considered to be the most important, and to make deductions about molecular
properties by consideration of them. For N 2 O, none of the nine Lewis structures of
Figure 2-8 alone can account for the similarity of the N-N and N-O bond-lengths
(1.13 and 1.19 Å) to those of triple and double bonds (1.10 and 1.20 Å – see
Section 2-3(b)). It is therefore hoped that resonance between the most stable of
these structures (i.e. those of lowest energy) will account for the observation. Two
ii Altogether, there are 27 other Lewis-type valence-bond structures that differ in the distributions of the four π- and four -electrons, and which participate in resonance with the octet
structures of Figure 2.9. These structures have fewer covalent bonds than have the octet structures. Here, we are restricting our attention to a consideraton of the octet structures because
these are usually the most useful for qualitative discussions of bonding. In Chapter 23, we
shall describe how to take account of the non-octet structures when constructing wavefunctions. See also Refs. 13a-d.
21
any bond that arises from electron sharing by two atoms. The concept of an energy
stabilization through resonance between two or more Lewis structures was
developed by Pauling and Slater in the early 1930s. For references to this period,
the reader is referred to Ref. (1b), p.184.
Lewis also suggested that when carbon, nitrogen, oxygen and fluorine atoms
are bonded to other atoms in a molecule, they tend to acquire the electron configuration of the inert gas neon. With a
2
2
6
1s 2s 2p ground-state configuration, the
neon atom has eight electrons in its valence shell. When they form covalent bonds,
atoms of the other elements above acquire this neon configuraton, by sharing their
unpaired electrons with the unpaired electrons of other atoms. According to
Lewis, stable (or low energy) valence-bond structures have eight valence-shell
electrons disposed around the atomic kernels (atomic nuclei + inner-shell electrons) for any of these first-row elements. Lewis and Langmuir respectively gave
the names of “rule of eight” and “octet rule” to this requirement. One quantum
mechanical justification for this rule is provided by the existence of four n = 2 atomic orbitals (namely 2s,
x
2p , y
2p , and z
2p ), and a maximum occupancy of two
electrons per orbital is permitted by the Pauli exclusion principle.
2-4(b) Standard Valence-Bond Theory and N 2 O
We shall now use the covalent molecule N 2 O to consider how the octet rule is
usually applied. For this molecule, there are nine Lewis structures (namely structures (1)-(9) of Figure 2-9) that have different π-electron distributions, and which
satisfy the octet rule. Each of these structures will contribute to the ground state
resonance description of the electronic structure
ii
. To provide a simple qualitative
discussion of the bonding, it is usual to select those valence-bond structures that
are considered to be the most important, and to make deductions about molecular
properties by consideration of them. For N 2 O, none of the nine Lewis structures of
Figure 2-8 alone can account for the similarity of the N-N and N-O bond-lengths
(1.13 and 1.19 Å) to those of triple and double bonds (1.10 and 1.20 Å – see
Section 2-3(b)). It is therefore hoped that resonance between the most stable of
these structures (i.e. those of lowest energy) will account for the observation. Two
ii Altogether, there are 27 other Lewis-type valence-bond structures that differ in the distributions of the four π- and four -electrons, and which participate in resonance with the octet
structures of Figure 2.9. These structures have fewer covalent bonds than have the octet structures. Here, we are restricting our attention to a consideraton of the octet structures because
these are usually the most useful for qualitative discussions of bonding. In Chapter 23, we
shall describe how to take account of the non-octet structures when constructing wavefunctions. See also Refs. 13a-d.